Upper Bound Analysis Of Collapsing Mechanism Of Surrounding Rock And Rockbolt Supporting Structures For Tunnels

The issue of tunnel stability is one of the essential problems in tunnel engineering. The assessment of tunnel stability when the supporting condition is known and the determination of potential failure surface for tunnel surrounding rock at critical state are especially important for scholars and engineers in their theoretical tunnel studies. There are limitations when the conventional soil mechanics and finite element method are employed to solve these problems. However, the application of the upper bound theorem of limit analysis in geotechnical stability analysis can not only derive the actual collapse load but also obtain the critical failure surface. Therefore, the upper bound theorem of limit analysis is one of the effective methods to solve the problems in tunnel engineering as mentioned above. Based on the upper bound theorem of limit analysis, using analytical and numerical methods, this dissertation studies the stability problems of deep and shallow tunnel for various complex factors. The main content of research is as follows:(1) By combining the strength reduction method with the upper bound theorem, the objective function of factor of safety for shallow tunnel is derived from reducing the original soil strength parameters and virtual work equation. Using the sequential quadratic programming to optimize the objective function, the upper bound solution of factor of safety for shallow tunnel is obtained and the assessment of tunnel stability is conducted.(2) Based on the collapse and blow-out failure mechanisms, the objective function of factor of safety for tunnel face is constructed by using the strength reduction method and the upper bound theorem. By introducing the influence factor of actual project into the upper bound analysis, the upper bound solution of factor of safety for tunnel face under each factor is obtained with the help of optimization calculation and the effect of parameters on the factor of safety is studied.(3) To illustrate the collapsing feature of surrounding rock for shallow tunnel roof, a two-dimensional curved failure mechanism is constructed. Using the Hoek-Brown failure criterion and the variational approach, the analytical solution of collapsing surface for surrounding rock over shallow tunnel roof is derived in the framework of upper bound theorem. Furthermore, by introducing the power of pore pressure as a power of external force in the virtual work equation, the upper solution for the shape of collapsing surface over deep tunnel roof subjected to pore pressure is obtained.(4) To achieve three-dimensional stability analysis for collapse block of a deep tunnel roof, a three-dimensional rotational failure mechanism is constructed. By calculating the rate of energy dissipation and the external rate of work in the failure mechanism, an objective function which includes the equation of collapsing surface is obtained. With the help of variational approach, the analytic expression of surface equation for the three-dimensional collapsing block is derived, and the shapes of three-dimensional collapsing surface for deep tunnel under different rock parameters are drawn.(5) By extending the three-dimensional stability analysis method for deep tunnel to shallow tunnel, the shapes of three-dimensional collapsing surface of shallow tunnel are derived. Considering the influence of different rock parameters, surcharge load, and supporting pressure on the shape of collapsing surface, the change law of each parameter for the shape of collapsing surface is obtained.(6) On the basis of the research results mentioned above, the analytical solution of collapsing surface for deep tunnel with the effect of rockbolt are derived from energy dissipation calculation and variational approach. By analyzing the size of collapsing block for deep tunnel under different rockbolt parameters, the change laws of each parameter for rockbolt are obtained.(7) Based on the observed geological data of running tunnel in Nanjing Metro, using numerical simulation and the analytical method mentioned above, the shape of collapsing surface for surrounding rock over tunnel roof is calculated, and the research results are thus applied to practical projects.